The question consists of four statements numbered "I, II, III and IV" given below it. You have to decide whether the data provided in any of the statement(s) alone is/are sufficient to answer the question. There are only three people in a family i.e. father, mother and a child. If present ages of father and mother are in the ratio 10:9, respectively, then find the present age of the child. Statement I: Ten years hence from now, the age of child will be 56% less than that of the father. Statement II: Present age of child is 70% less than that of the father and 24 years less than that of the mother. Statement III: Six years ago from now, the age of mother was 5 times the age of child. Six years hence from now, the age of father will be 28 years more than that of child. Statement IV: Difference between present age of mother and father is 4 years and difference between present age of child and mother is 24 years.

Explanation

4 Detailed solution: Let the present ages of mother and father be '9x' years and '10x' years, respectively. Statement I: Let the present age of child be 'y' years. According to the statement: (10x + 10) X 0.44 = y Or, 4.4x + 4.4 = y Since, there are two variables and only one equation, it is impossible to find the unique values. So, data in statement I alone is not sufficient to answer the question. Statement II: According to the statement: Present age of child = 10x X 0.3 = '3x' years 3x + 24 = 9x Or, 6x = 24 So, x = 4 So, present age of child = 3x = 3 X 4 = 12 years So, data in statement II alone is sufficient to answer the question. Statement III: Present age of the child = (10x - 28) years Six years ago from now, age of the child = (10x - 28 - 6) = (10x - 34) years According to the statement: 9x - 6 = 5 (10x - 34) Or, 9x - 6 = 50x – 170 41x = 164 So, x = 4 So, present age of child = 10x - 28 = 10 X 4 - 28 = 12 years So, data in statement III alone is sufficient to answer the question. Statement IV: According to the statement: 10x - 9x = 4 Or, x = 4 So, present age of mother = 9 X 4 = 36 years So, present age of child = 36 - 24 = 12 years So, data in statement IV alone is sufficient to answer the question.